TITLE:
On Simple Completely Reducible Binary-Lie Superalgebras over sl2(F)
AUTHORS:
Manuel Arenas
KEYWORDS:
Binary-Lie, Super-Algebras
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.5,
April
20,
2015
ABSTRACT: In this article, we prove that if B is a simple binary-Lie superalgebra whose even part is
isomorphic to sl2(F) and whose odd part is a completely reducible
binary-Lie-module over the even part, then B is a Lie superalgebra. We introduce also a binary-Lie
module over which is sl2(F) not completely reducible.